\section{Measures}
In this section, we discuss the different measures used for computing the pair-wise similarity between languages of
WALS data.

\begin{table}[hbt]
\linespread{1.6}
\begin{minipage}[t]{0.38\textwidth} \footnotesize
\begin{center}
\begin{tabular}{|l|c|}
\hline
\multicolumn{2}{|c|}{\bf Vector similarity} \\ 
\hline
euclidean & $\sqrt[2]{\Sigma_{i=1}^{n} (v_1^i-v_2^i)^2}$ \\
seuclidean & $\Sigma_{i=1}^{n} (v_1^i-v_2^i)^2$ \\
nseuclidean & $\dfrac{\norm{\sigma_1-\sigma_2}}{2*\norm{\sigma_1}+\norm{\sigma_2}}$ \\
manhattan & $\Sigma_{i=1}^{n} \abs{v_1^i-v_2^i}$ \\
chessboard & $max((v_1^i-v_2^i) \forall i\in (1, n))$\\
braycurtis & $\dfrac{\Sigma_{i=1}^{n} \abs{v_1^i-v_2^i}}{\Sigma_{i=1}^{n} \abs{v_1^i+v_2^i}}$ \\
%canberra &
cosine & $\dfrac{v_1\cdot v_2}{\norm{v_1}*\norm{v_2}}$ \\
correlation & $1-\dfrac{\sigma_1\cdot \sigma_2}{\norm{\sigma_1}*\norm{\sigma_2}}$ \\
\hline
\end{tabular}
\end{center}
\end{minipage}
\begin{minipage}[t]{0.62\textwidth} \footnotesize
\begin{center}
\begin{tabular}{|l|c|}
\hline
\multicolumn{2}{|c|}{\bf Boolean similarity} \\ 
\hline
hamming & $\#_{\ne 0}(v_1 \XOR v_2)$ \\
jaccard & $\dfrac{\#_{\ne 0}(v_1 \XOR v_2)}{\#_{\ne 0}(v_1 \XOR v_2)+\#_{\ne 0}(v_1 \& v_2)}$ \\
tanimoto & $\dfrac{2*\#_{\ne 0}(v_1 \XOR v_2)}{\#_{\ne 0}(v_1 \& v_2)+\#_{= 0}(v_1 \| v_2)+2*\#_{\ne 0}(v_1 \XOR v_2)}$ \\
matching & $\dfrac{\#_{\ne 0}(v_1 \XOR v_2)}{\#v_1}$ \\
dice & $\dfrac{\#_{\ne 0} (v_1 \XOR v_2)}{\#_{\ne 0} (v_1 \XOR v_2) + 2*\#_{\ne 0} (v_1 \& v_2)}$ \\
sokalsneath & $\dfrac{2*\#_{\ne 0} (v_1 \XOR v_2)}{2*\#_{\ne 0} (v_1 \XOR v_2) + \#_{\ne 0} (v_1 \& v_2)}$ \\
russellrao & $\dfrac{\#_{\ne 0} (v_1 \XOR v_2)+\#_{= 0} (v_1 \| v_2)}{\# v_1}$ \\
yule & $\dfrac{2*\#_{\ne 0} (v_1 - v_2)*\#_{= 0} (v_1 - v_2)}{\#_{\ne 0} (v_1 - v_2)*\#_{= 0} (v_1 - v_2) + \#_{\ne 0} (v_1 \& v_2)*\#_{= 0} (v_1 \| v_2)}$ \\
\hline
\end{tabular}
\end{center}
\end{minipage}
\end{table}
